# Too Many Angles, Too Little Information

Geometry Level 3

In a triangle $$ABC$$, the measures of the angles are $$\angle A=30^\circ,$$ $$\angle B=80^\circ.$$ Point $$M$$ lies inside the triangle, such that $$\angle MAC = 10^\circ,$$ $$\angle MCA = 30^\circ.$$ What is the measure (in degrees) of $$\angle BMC?$$

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